“…The solution of Eq. ( 37) can be carry out by iteration method, analogous to known Chandrasekhar's (1960) method (see also Dementyev (2008)). For values of parameter β we chose β = 0.001, 0.01, 0.05.…”
Section: The Results Of Calculationsmentioning
confidence: 99%
“…The effective methods of numerical calculation of Ĥ -matrix are presented in papers Krease & Siewert (1971) , Rooij et al(1989) and Dementyev (2008).…”
Section: Solution Of Integral Equation For S(τ ) Using Resolvent Matrixmentioning
confidence: 99%
“…The problems with non-isotropic and polarized radiation are more difficult to consider (see, for example, Stenflo 1976, Rees & Saliba 1982Faurobert 1988, Faurobert-Sholl & Frisch 1989; Faurobert-Sholl et al 1997). It should be also noted the papers by Ivanov 1996, Ivanov et al 1997, and Dementyev 2008, 2010. Simple quantum mechanical study of the resonance line problems is given in the standard text-book by Landau & Lifshitz vol.…”
We study the standard spectral line radiative transfer equation for media consisting of resonant atoms and non-resonant components (the dust grains and the atoms without considered spectral transition). Our goal is to study the intensity and polarization of the resonance radiation emerging from semi-infinite atmosphere. Using the known technique of resolvent matrices, we obtain the exact solution of vectorial radiative transfer equation for various sources of non-polarized radiation in semi-infinite atmosphere. Homogeneous, linear increasing and exponentially decreasing sources are considered. Recall, that' with the homogeneous sources correspond to the isothermal atmosphere and the exponential ones correspond to the incident radiation with different angles of inclination.
“…The solution of Eq. ( 37) can be carry out by iteration method, analogous to known Chandrasekhar's (1960) method (see also Dementyev (2008)). For values of parameter β we chose β = 0.001, 0.01, 0.05.…”
Section: The Results Of Calculationsmentioning
confidence: 99%
“…The effective methods of numerical calculation of Ĥ -matrix are presented in papers Krease & Siewert (1971) , Rooij et al(1989) and Dementyev (2008).…”
Section: Solution Of Integral Equation For S(τ ) Using Resolvent Matrixmentioning
confidence: 99%
“…The problems with non-isotropic and polarized radiation are more difficult to consider (see, for example, Stenflo 1976, Rees & Saliba 1982Faurobert 1988, Faurobert-Sholl & Frisch 1989; Faurobert-Sholl et al 1997). It should be also noted the papers by Ivanov 1996, Ivanov et al 1997, and Dementyev 2008, 2010. Simple quantum mechanical study of the resonance line problems is given in the standard text-book by Landau & Lifshitz vol.…”
We study the standard spectral line radiative transfer equation for media consisting of resonant atoms and non-resonant components (the dust grains and the atoms without considered spectral transition). Our goal is to study the intensity and polarization of the resonance radiation emerging from semi-infinite atmosphere. Using the known technique of resolvent matrices, we obtain the exact solution of vectorial radiative transfer equation for various sources of non-polarized radiation in semi-infinite atmosphere. Homogeneous, linear increasing and exponentially decreasing sources are considered. Recall, that' with the homogeneous sources correspond to the isothermal atmosphere and the exponential ones correspond to the incident radiation with different angles of inclination.
“…( 85) has been investigated in detail in several earlier papers (see e.g. Ivanov et al 1997aIvanov et al , 1997bDementyev 2008). For a more complete list of references we refer the reader to Faurobert-Scholl & Frisch (1989) and reviews by Nagendra (2003) and Nagendra & Sampoorna (2009).…”
Section: Polarization Of Resonant Radiation In a Model Of Full Freque...mentioning
confidence: 98%
“…For investigation of multiple scattering of resonant radiation one uses the matrix transfer equation of the general form (see, for example, Hummer 1962; Ivanov et al 1997aIvanov et al , 1997bDementyev 2008):…”
Section: The Case Of Resonant Scatteringmentioning
Freely oriented small anisotropic grains and molecules depolarize radiation both in single scattering and in the process of multiple scattering. Especially large depolarization occurs for resonant scattering corresponding to the electron transitions between the energy levels with very different quantum numbers. The existence of light absorption also changes essentially the angular distribution and polarization of radiation, outgoing from an atmosphere. In the present paper we consider these effects in detail both for continuum radiation and for resonant lines. Because the term describing the depolarization deals with isotropic radiation, we consider the axially symmetric part of radiation. We derived the formulas for observed intensity and polarization using the invariance-principles both for continuum and resonant scattering. We confine ourselves to two problems -the diffuse reflection of the light beam from semi-infinite atmosphere, and the Milne problem.
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